Question

On any given​ day, a salesman can earn​ $0 with a 45​% ​probability, ​$250 with a 25​% ​probability, or ​$400 with a 30​% probability. His expected earnings​ equal: ​$ nothing ​(round your answer to the nearest penny​).

Answer 1

Answer: $ 182.5

Explanation:

The expected value of occurring events
`x_1,\ x_2, \ x_3\ ....,x_n` having probabilities
`p_1,\ p_2,\ p_3\ ....,p_n` is given by :-

`E(x)=x_1\cdot \ p_1+x_2\cdot \ p_2+x_3\cdot \ p_3+....+x_n\cdot \ p_n`

Given : On any given​ day, a salesman can earn​ $0 with a 45​% ​probability, ​$250 with a 25​% ​probability, or ​$400 with a 30​% probability.

i.e. Probability of earning $0 = 0.45

Probability of earning $250=0.25

Probability of earning $400=0.30

Then , the expected earnings​ is given by :-

`E(x)=0*0.45+250*0.25+400*0.30=182.5`

Hence, the his expected earnings​ is $182.5.